If you would like to prevent users from using emojis in your community, head over to your community settings page. The setting is located here:
Community Settings --> Customization --> Look & Feel --> Customize Site Behavior --> Miscellaneous --> "Support Emojis in your community" --> OFF
Is it possible to turn-off specific emojis?
Yes, you can select specific emojis from not showing in emojis list by filtering them. This can be located and saved from Community Settings --> Security --> Access Restriction--> Curse Filtering --> Emoji Curse Filtering
Note: Similar to text based Curse Filter, add only one emoji per line.